Using Pythagoras, probably.

Lay the triangle on its side and draw the perpendicular height you're supposed to find. Then you got 2 right angle triangles.

Let h be the perp height and c = a+b be the length of the base (where a and b are the lengths to the perpendicular h.

Then you have two equations where are the lengths of the sloping sides.

Can you draw it? I can't be bothered myself, it's too much like hard work for me.